As it stands right now the SoftwareInputPanelRequest event isn't sent on QWebPage::handleSoftwareInputPanel(). That prevents the input method from coming on on S60. But there may be more issues.
http://trac.webkit.org/changeset/50801 fixes the issue in WebKit. The remaining brokeness is somewhere in QGraphicsView, as the issue is also reproducible without WebKit but a simple QGraphicsTextItem instead. The latest investigation shows that the graphicsview's viewport is the focus widget known to the input method, which of course means that the calls to inputMethodQuery() will not end up in QGraphicsView::inputMethodQuery() and therefore never reach the focused graphics item in the scene. Closing this bug nevertheless as the WebKit part is fixed.